Ch12_Summary - bee29400_ch12_727-753.indd Page 746...

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746 REVIEW AND SUMMARY This chapter was devoted to Newton’s second law and its application to the analysis of the motion of particles. Denoting by m the mass of a particle, by o F the sum, or resultant, of the forces acting on the particle, and by a the acceleration of the particle relative to a newtonian frame of reference [Sec. 12.2], we wrote o F 5 m a (12.2) Introducing the linear momentum of a particle, L 5 m v [Sec. 12.3], we saw that Newton’s second law can also be written in the form o F 5 L ˙ (12.5) which expresses that the resultant of the forces acting on a particle is equal to the rate of change of the linear momentum of the particle . Equation (12.2) holds only if a consistent system of units is used. With SI units, the forces should be expressed in newtons, the masses in kilograms, and the accelerations in m/s 2 ; with U.S. customary units, the forces should be expressed in pounds, the masses in lb · s 2 /ft (also referred to as slugs ), and the accelerations in ft/s 2 [Sec. 12.4]. To solve a problem involving the motion of a particle, Eq. (12.2) should be replaced by equations containing scalar quantities [Sec. 12.5]. Using rectangular components of F and a , we wrote o F x 5 ma x o F y 5 y o F z 5 z (12.8) Using tangential and normal components , we had © F t 5 m dv dt © F n 5 m v 2 r (12.9 9 ) We also noted [Sec. 12.6] that the equations of motion of a particle can be replaced by equations similar to the equilibrium equations used in statics if a vector 2 m a of magnitude ma but of sense oppo- site to that of the acceleration is added to the forces applied to the particle; the particle is then said to be in dynamic equilibrium . For the sake of uniformity, however, all the Sample Problems were solved by using the equations of motion, first with rectangular components [Sample Probs. 12.1 through 12.4], then with tangential and normal components [Sample Probs. 12.5 and 12.6].
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This note was uploaded on 12/05/2011 for the course MEEG 374 taught by Professor Ib during the Fall '11 term at The Petroleum Institute.

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Ch12_Summary - bee29400_ch12_727-753.indd Page 746...

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